Preprocessing

Every catalog page is a high-resolution jpeg-encoded scanned image, e.g. the first page of the 1950 catalog:

Figure: The front page of IKEA’s first catalog.

The idea is to use the raw pixels of each such image to generate data for visualization. Since it takes many days of cpu-time to process everything (19225 pages!), by necessity, the output from the preprocessing steps is what will be used here. All of the necessary R code for reproducing the results can be found in the accompanying Github repo and R package colorhull.

Pixels and colors

Each pixel in the 8-bit RGB color space has 16.7 million unique combinations. The catalogs are 200-300 pages long where each page often use far beyond 100000 colors. How do we even begin to organize or transform this in order to be able to visualize it in a meaningful way?

Mean colors over time

An obvious starting point is to just find the average color for each page.

years <- 1950L:2021L
n_colors <- 1
tile_size <- c(24, 3)
x_offset <- 45
max_n_pages <- 390

# Create pixel array and fill with default background color.
ar <- array(
  1,
  c(
    length(years) * n_colors * tile_size[[1]],
    x_offset + tile_size[[2]] * max_n_pages,
    3
  )
)
ar[, , 1] <- 1
ar[, , 2] <- 1
ar[, , 3] <- 248 / 255

# Draw a colored tile per page, per year.
y <- 1
for (year in years) {
  load(paste0("./data/stats", year, ".RData"))
  mean_colors <- lapply(stats_list, function(x) x$rgb_mean)
  x <- x_offset
  for (col in rep(mean_colors, each = tile_size[[2]])) {
    ar[y:(y + n_colors * tile_size[[1]] - 1), x, 1:3] <-
      rep(col, each = tile_size[[1]])
    x <- x + 1
  }
  y <- y + n_colors * tile_size[[1]]
}

im <- image_read(ar) %>%
  image_convert(matte = FALSE, depth = 16)
y <- 4
for (year in years) {
  im <- image_annotate(
    im,
    year,
    size = 18,
    color = "black",
    gravity = "northeast",
    location = paste0("+", tile_size[[2]] * max_n_pages + 5, "+", y)
  )
  y <- y + n_colors * tile_size[[1]]
}
im

Figure: Mean colors per page, per catalog. Front pages to the left.

The 1950-1955 catalogs are actually mostly sepia colored but the rest of the catalogs are more colorful than indicated by this visualization. It does not seem like mean colors say much about color popularity over time but there are a few things to note:

• Something happens with the design in the 1989 and 1990 catalogs followed by what looks like a reversal to the design before 1989.
• In 2002, colors suddenly become brighter and more vivid, which is continued up to the 2021 catalog. It also seems there are more pages with one principal, strong color rather than most pages having many colors (which is likely why the majority of the mean colors tend to brown).

All in all, a step up in terms of visualization is needed.

Color themes over time

Another approach is summarizing the colors of each page individually into what is usually called a theme. Quite surprisingly, the state of the art method for generating themes is essentially to use human artists.

⊕ Figure: RGB cube (Wikipedia).

When googling “finding dominant colors of an image” the results will include many tutorials applying the method k-means clustering to the problem. If one takes the \((R, G, B) / 255\) triples of an image, the result is a point cloud where points close to each other have similar colors. K-means will find \(k\) centers where each point is assigned to its nearest center. Once the algorithm has converged, these centers form a set of principal colors.

This is a fine method, if not for a number of edge cases. First, the outcome is heavily influenced by its random initialization so lacks a guarantee of finding the optimum clustering. Second, even if it did find one, it might not correspond to a perceptual optimum. This can be easily illustrated:

im <- image_read("images/page50-1989.jpg") %>%
  # Point resizing method produces visually bad results but does not introduce
  # interpolated colors that was not part of the image from the start.
  image_resize("25%", filter = "Point")
im_rgb <- im %>%
  image_data("rgb") %>%
  as.numeric()
d <- dim(im_rgb)
im_rgb <- array_reshape(im_rgb, c(d[[1]] * d[[2]], 3))
clustering <- kmeans(im_rgb, centers = 6, iter.max = 50)
plot_theme(im, clustering$centers)

Theme for page 50 of the 1989 catalog, generated by k-means clustering.

For a human, this six-color theme is likely missing two important colors: the green from the sofa and the red from the toy vehicle. Without these, the theme does not really capture the perceptual qualities of the page. Note that it also misses the blue carpet and the yellow of the toy although it could be argued that’s a good thing.

This subjective trade-off is essentially the problem with all existing methods.

⊕The paper had me fooled with a promise of a 48 line Python implementation but eventually it turned out that the part needed was more complex. I re-implemented the theme generation part in R (much easier said than done!) with some minor additions like sorting themes according to the LMS color space in order for easier comparison between two themes (note that sorting by LMS is far from an obvious choice but it gave consistent enough results.)

After a long search, a paper by Tan, Echevarria and Gingold, “Efficient palette-based decomposition and recoloring of images via RGBXY-space geometry” (2018) emerged with a promising and intuitive idea, based on the observation that color distributions of paintings and natural images often take on a convex shape in RGB space. Thus, forming a point cloud from the RGB triples, one can proceed to find its convex hull. That is, the smallest triangulated mesh that fits all points. The vertices of the hull are the colors that quite literally stick out (makes the mesh convex).

⊕ Figure: Example of convex hull after repeated edge collapses. The arrow points to large volume loss when going from a hull composed of 5 vertices to one with four vertices (source: Tan et al., 2016).

One can then proceed to look at each edge of the hull and see how much volume would be lost if removed and replaced by a single vertex. The edge with the smallest volume-loss can be removed and still have similar colors left. If repeated until the desired amount of vertices/colors are obtained, one should end up with the colors that most define the image.

⊕An important detail here is that interpolation during resizing introduces many new colors and can have a large effect on the outcome. Without interpolation, the resized images look bad to a human but in this case moiré and other visual artefacts does not matter. Also, since this method only indirectly take into account the amount colors are used, a single red pixel in an otherwise blue picture could potentially affect the outcome. The decision was to resize the images to about 10% of their initial size in order to lose smaller elements like vividly colored books in book cases, etc.

I have compiled this work into the R package colorhull (work in progress). This is the result on the same page as above:

color_theme <- get_theme_colors_from_image("images/page50-1989.jpg", n_colors = 6)
plot_theme(im, color_theme)

Theme for page 50 of the 1989 catalog, generated by convex hull-based method.

I would argue that this result is much better than with k-means but at the same time, a potential problem might be that it picks up colors that is not central to the image (i.e. the yellow and blue colors).

Here are the generated themes for every page in every catalog:

years <- 1950L:2021L
n_colors <- 8
tile_size <- 3
x_offset <- 45
max_n_pages <- 390

# Initialize pixel array.
ar <- array(
  1,
  c(
    length(years) * n_colors * tile_size,
    x_offset + tile_size * max_n_pages,
    3
  )
)
ar[, , 1] <- 1
ar[, , 2] <- 1
ar[, , 3] <- 248 / 255

# Fill array with one tile per color, per page, per year.
y <- 1
for (year in years) {
  load(paste0("./data/colors", year, ".RData"))
  x <- x_offset
  for (theme in rep(rgb_list, each = tile_size)) {
    d <- dim(theme)[1]
    if (d < n_colors) {
      extra <- matrix(rep(theme[d,], n_colors - d), ncol = 3)
      theme <- rbind(theme, extra)
    }
    ar[y:(y + n_colors * tile_size - 1), x, 1:3] <- rep(theme, each = tile_size)
    x <- x + 1
  }
  y <- y + n_colors * tile_size
}

im <- image_read(ar) %>%
  image_convert(matte = FALSE, depth = 16)
y <- 4
for (year in years) {
  im <- image_annotate(
    im,
    year,
    size = 18,
    color = "black",
    gravity = "northeast",
    location = paste0("+", tile_size * max_n_pages + 5, "+", y)
  )
  y <- y + n_colors * tile_size
}
im

Figure: 8-color themes for the 1950-2020 catalogs using a convex hull- based method. Front pages to the left.

As before, this experiment did not pan out as clear as I hoped in terms of trends over time. Rather than using a limited color scheme for each page, it looks like most pages are composed of many colors and all themes have a little of everything. This is interesting in itself but given that we know that the interior design ideals of the 1970’s were very different from those of the 1990’s, this visualization is not picking up the differences in an obvious way.

There are a few interesting details though:

1. The colors per catalog follow a quite even distribution in terms of luminosity and saturation. If there are vivid colors in some pages, most pages of the catalog have this property (and vice versa with muted colors). Some of this is likely a result of the way catalogs are scanned, often not being true to the original printed colors.

2. In 2002-2003, IKEA really boosted colors:

   
   

   Page 49 of the 2002 catalog.
   

   After 2003, the colors were toned down but are still much more vivid than up to 2001. It looks like saturation is rising toward 2020 and this is something that can be explored further (see below).

3. IKEA often uses bright colored overlays indicating, for example, if a product is new (“Nyhet!”). This can be seen most clearly in the reds throughout the 1989-1990 catalogs.

4. Although the interiors IKEA showcase are styled, they also set out to be realistic, capturing the wide array of colors represented in our homes. This makes it difficult to summarize the use of colors using a limited palette.

Saturation over time

If not by color then perhaps general trends could be found by looking at saturation, or vividness, alone? Here, using a more objective metric would enable us to see if the data backs the intuition in (2), above.

⊕There are multiple definitions of saturation. E.g. if starting with a maximally saturated blue color and mixing in white, does that affect saturation or not? Does mixing in black affect saturation? Perceptually, most people tend to agree on a bright green being more saturated than black and white. HSV and HSL color spaces are problematic in this regard but are also easy to work with. Using HSV at least avoids the problem of white being maximally saturated.

Saturation can be calculated by converting each pixel value from the RGB to HSV color space and extracting the S channel. This is then used to calculate pooled means and standard deviations for confidence intervals.

⊕It should also be noted that saturation is not necessarily perceptually linear between different hues or luminosities. Thus, using the mean saturation is potentially problematic but the alternatives seem to be far more complex.

If the confidence intervals are narrow, this would be evidence towards that (1), above, holds.

years <- 1950L:2021L
mean_df <- tibble(year = integer(), pooled_mean = numeric(), ci = numeric())
for (year in years) {
  # The data loaded is e.g. mean saturation per page so we need to weigh/pool
  # this according to the number of pixels on each page in order to get one
  # value to plot for the entire catalog/year.
  load(paste0("./data/stats", year, ".RData"))
  denominator <- reduce(stats_list, function(x, y) x + y$n_pixels, .init = 0)
  pooled_mean <- reduce(
    stats_list,
    function(x, y) x + y$saturation_mean * y$n_pixels,
    .init = 0
  ) / denominator

  pooled_sd <- sqrt(
    reduce(
      stats_list,
      function(x, y) x + y$saturation_sd^2 * (y$n_pixels - 1),
      .init = 0
    ) / (denominator - length(stats_list))
  )
  ninv <- sqrt(
    reduce(stats_list, function(x, y) x + 1 / y$n_pixels, .init = 0)
  )

  mean_df <- mean_df %>%
    add_row(
      year = year,
      pooled_mean = pooled_mean,
      ci = 1.96 * pooled_sd * ninv
    )
}

mean_df %>%
  ggplot(aes(x = year, y = pooled_mean)) +
  geom_line(color = "#C4961A") +
  geom_ribbon(
    aes(ymin = pooled_mean - ci, ymax = pooled_mean + ci),
    fill = "#C4961A",
    alpha = 0.25
  ) +
  geom_vline(xintercept = 1991, linetype = 2, color = "gray") +
  annotate(
    "text",
    label = "1991",
    x = 1991,
    y = 0.1,
    angle = 90,
    hjust = 0,
    vjust = 1.5,
    colour = "gray"
  ) +
  xlab("Year") +
  ylab("Saturation") +
  theme_tufte(base_family = "sans") +
  theme(
    panel.background = element_rect("#fffff8", NA),
    plot.background = element_rect(fill = "#fffff8", NA)
  )

Figure: Pooled mean saturation over time (with 95% confidence interval.)

Turns out that peak saturation was actually at 1991… and perhaps there is something to it:

Page 158 of the 1991 catalog.

More surprising is that saturation during the late 2010’s is lower than almost all other periods, which is not apparent from the theme visualization. That the saturation is lower than during the 1950’s is due to the earliest catalogs being sepia colored.

Overall, it is likely that the abundant use of black and white in the catalogs is affecting the outcome too much to draw general conclusions from but at least it’s picking up on the dip in saturation in the 2021 catalog:

Page 22 of the 2021 catalog.

Prologue

Even though the IKEA catalogs from the 1970’s are distinctly different from the catalogs in the 1990’s, it seems non-trivial to visualize these differences by just using color. That IKEA caters to everyone and not everyone wants the same thing at the same time does not help with picking up trends either:

Page 2 vs page 73 in the 1969 catalog.